# std::add_sat

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< cpp‎ | numeric

Defined in header `<numeric>` |  |
template< class T > constexpr T add_sat( T x, T y ) noexcept; |  | (since C++26)

Computes the saturating addition x + y. This operation (unlike built-in arithmetic operations on integers) behaves as-if it is a mathematical operation with an infinite range. Let `q` denote the result of such operation. Returns:

- `q`, if `q` is representable as a value of type `T`. Otherwise,
- the largest or smallest value of type `T`, whichever is closer to the `q`.

This overload participates in overload resolution only if `T` is an integer type, that is: signed char, short, int, long, long long, an extended signed integer type, or an unsigned version of such types. In particular, `T` must not be (possibly cv-qualified) bool, char, wchar_t, char8_t, char16_t, and char32_t, as these types are not intended for arithmetic.

### Parameters

x, y | - | integer values

### Return value

Saturated x + y.

### Notes

Unlike the built-in arithmetic operators on integers, the integral promotion does not apply to the x and y arguments.

If two arguments of different type are passed, the call fails to compile, i.e. the behavior relative to template argument deduction is the same as for std::min or std::max.

Most modern hardware architectures have efficient support for saturation arithmetic on SIMD vectors, including SSE2 for x86 and NEON for ARM.

Feature-test macro | Value | Std | Feature
--- | --- | --- | ---
`__cpp_lib_saturation_arithmetic` | `202311L` | (C++26) | Saturation arithmetic

### Possible implementation

See libstdc++ (gcc).

### Example

Can be previewed on Compiler Explorer.

Run this code

    #include <climits>
    #include <limits>
    #include <numeric>

    static_assert(CHAR_BIT == 8);
    static_assert(UCHAR_MAX == 255);

    int main()
    {
        constexpr int a = std::add_sat(3, 4); // no saturation occurs, T = int
        static_assert(a == 7);

        constexpr unsigned char b = std::add_sat<unsigned char>(UCHAR_MAX, 4); // saturated
        static_assert(b == UCHAR_MAX);

        constexpr unsigned char c = std::add_sat(UCHAR_MAX, 4); // not saturated, T = int
            // add_sat(int, int) returns int tmp == 259,
            // then assignment truncates 259 % 256 == 3
        static_assert(c == 3);

    //  unsigned char d = std::add_sat(252, c); // Error: inconsistent deductions for T

        constexpr unsigned char e = std::add_sat<unsigned char>(251, a); // saturated
        static_assert(e == UCHAR_MAX);
            // 251 is of type T = unsigned char, `a` is converted to unsigned char value;
            // might yield an int -> unsigned char conversion warning for `a`

        constexpr signed char f = std::add_sat<signed char>(-123, -3); // not saturated
        static_assert(f == -126);

        constexpr signed char g = std::add_sat<signed char>(-123, -13); // saturated
        static_assert(g == std::numeric_limits<signed char>::min()); // g == -128
    }

### See also

sub_sat (C++26) | saturating subtraction operation on two integers (function template)
mul_sat (C++26) | saturating multiplication operation on two integers (function template)
div_sat (C++26) | saturating division operation on two integers (function template)
saturate_cast (C++26) | returns an integer value clamped to the range of another integer type (function template)
clamp (C++17) | clamps a value between a pair of boundary values (function template)
in_range (C++20) | checks if an integer value is in the range of a given integer type (function template)
min [static] | returns the smallest finite value of the given non-floating-point type, or the smallest positive normal value of the given floating-point type (public static member function of `std::numeric_limits<T>`)
max [static] | returns the largest finite value of the given type (public static member function of `std::numeric_limits<T>`)

### External links

1. | A branch-free implementation of saturation arithmetic — Locklessinc.com, 2012
2. | C++ Weekly - Ep 459 - C++26's Saturating Math Operations — Youtube.com, 2024-12-16

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